Revisiting Cardassian model and cosmic constraint

Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In the non-relativistic limit (x???x,t??t,???0), the boundary conformal algebra changes to boundary Galilean conformal algebra (BGCA). In this work, some aspects of AdS/BCFT in the non-relativistic limit were explored. We constrain correlation functions of Galilean conformal invariant fields with BGCA generators. For a situation with a boundary condition at surface x=0 ( $z=\overline{z}$ ), our result agrees with the non-relativistic limit of the BCFT two-point function. We also introduce the holographic dual of boundary Galilean conformal field theory.     

Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.     

Holographic renormalization of foliation preserving gravity and trace anomaly

From the holographic renormalization group viewpoint, while the scale transformation plays a primary role in holographic dualities by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomorphic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four dimension predicts the Ricci scalar squared term that would be incompatible with the Wess–Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomorphic theory of gravity could be in conflict with a theorem of the dual unitary quantum field theory.     

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.     

Holography and entanglement in flat spacetime

We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly nonlocal. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a nonlocal scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotically flat spacetimes.     

Entropy of Kaluza–Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza–Klein black hole in Einstein–Maxwell–Dilaton theory. For the extremal Kaluza–Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein–Hawking entropy of extremal Kaluza–Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza–Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza–Klein black hole is reproduced by Cardy formula.     

Higher derivative corrections in holographic Zamolodchikov–Polchinski theorem

We study higher derivative corrections in holographic dual of Zamolodchikov–Polchinski theorem that states the equivalence between scale invariance and conformal invariance in unitary d-dimensional Poincaré invariant field theories. From the dual holographic perspective, we find that a sufficient condition to show the holographic theorem is the generalized strict null-energy condition of the matter sector in effective (d+1)-dimensional gravitational theory. The same condition has appeared in the holographic dual of the “c-theorem” and our theorem suggests a deep connection between the two, which was manifested in two-dimensional field theoretic proof of the both.     

Lifting a conformal field theory from d-dimensional flat space to (d+1)-dimensional AdS space

A quantum field theory on anti-de Sitter space can be constructed from a conformal field theory on its boundary Minkowski space by an inversion of the holographic mapping. The resulting theory is defined by its Green functions and is conformally covariant. The structure of operator product expansions is carried over to AdS space. We show that this method yields a higher spin field theory HS(4) from the minimal conformal O(N) sigma model in three dimensions.     

Boundary entropy can increase under bulk RG flow

The boundary entropy log(g)$\log (g)$ of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g   due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g)$\log (g)$ can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

Holographic forced fluid dynamics in non-relativistic limit

We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss–Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of gravitational field equations. We use the non-relativistic fluid expansion method to study the Einstein–Maxwell-dilaton system with a negative cosmological constant, and obtain the holographic incompressible forced Navier–Stokes equations of the dual fluid at AdS boundary and at a finite cutoff surface, respectively. The concrete forms of external forces are given.     

Conformally coupled scalars, instantons, and vacuum instability in 4D anti-de Sitter space

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory. The holographic effective potential is exactly calculated, allowing us to study nonperturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.     

Hidden conformal symmetry of rotating black holes in the five-dimensional Gödel universe

We have investigated the hidden conformal symmetry of generic non-extremal rotating black holes in the five-dimensional Gödel universe. In a range of parameters, the low-frequency massless scalar wave equation in the “near region” can be described by an SL(2, R) _L × SL(2, R) _R conformal symmetry. We further found that the microscopic entropy via Cardy formula matches the macroscopic Bekenstein-Hawking entropy and the absorption cross section for the massless scalar also agrees with the one for the two dimensional finite temperature conformal field theory (CFT). All these evidences support the conjecture that the generic non-extremal rotating black hole immersed in the Gödel universe can be dual to a two dimensional finite temperature CFT. In addition, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the rotating Gödel-type black holes into the forms of conformal thermodynamics.     

Anti-de Sitter-space/conformal-field-theory Casimir energy for rotating black holes

We show that, if one chooses the Einstein static universe as the metric on the conformal boundary of Kerr-anti-de Sitter spacetime, then the Casimir energy of the boundary conformal field theory can easily be determined. The result is independent of the rotation parameters, and the total boundary energy then straightforwardly obeys the first law of thermodynamics. Other choices for the metric on the conformal boundary will give different, more complicated, results. As an application, we calculate the Casimir energy for free self-dual tensor multiplets in six dimensions and compare it with that of the seven-dimensional supergravity dual. They differ by a factor of 5/4.     

Holographic entropy bound and local quantum field theory

I show how the holographic entropy bound can be derived from elementary flat-spacetime quantum field theory when the total energy of Fock states is constrained gravitationally. This energy constraint makes the Fock space dimension (whose logarithm is the maximum entropy) finite for both bosons and fermions. Despite the elementary nature of my analysis, it results in an upper limit on entropy in remarkable agreement with the holographic bound, and also provides a microscopic deviation of a more general entropy bound recently introduced by Gour.